How casinos make money: why the house always wins, even on the nights you win
The law of large numbers: why the casino always wins, even when players win
Tonight, about one player in three who bets on red at roulette walks out ahead. Yet the casino knows quite closely what it will win this month. How can both be true?
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1
The next morning, you ask Rono why your win did not worry him. He shows you the casino floor. Roulette tables spin there side by side, every night of the year, and each one takes bet after bet.
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2
Picture 100 players who each bet $10 on red, again and again. After 10 bets, or even 100, about a third of them are ahead, like you last night. After 1,000 bets, only about 19 are. After 10,000 bets, almost nobody is: about 3 players in 1,000.
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3
Look at your own money, bet after bet. In the first bets, it jumps up and down. Luck is large compared with the few dollars you have bet. Over thousands of bets, luck still comes and goes. But the 2.7 cents taken from every dollar keep adding up, and in the end they weigh more than luck. So the more bets there are, the closer the result comes to the average.
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4
Now think of the casino. It gets the bets of all its players. Say that in one month, its players make a million bets of $10 on red. On average, the casino keeps $270,000. Almost every month, it keeps between $237,000 and $303,000. This is the law of large numbers: over many tries, the result comes close to the average. For the casino, the house edge is no longer luck.
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5
So Rono does not need you to lose tonight. He needs you, and everyone else, to keep playing. Next door, a whole room of machines is built for just that.
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Quick check
Two casinos with the same games.
Show the answer
The one with 1,000 tables. It takes far more bets, so its result comes closer to the house edge, and luck matters less.
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Go further
The name for the average.